Janice makes a peanut butter and jam sandwich. One-quarter of the total amount of filling is jam. And the rest is peanut butter. Circle the ratio of jam to peanut butter in the sandwich. Is it one to three, one to four, three to four, or one to five?
One-quarter is jam. And that means the fraction of jam to total filling is one over four. One-quarter written as a fraction is one-fourth. If we know that the rest of the sandwich is filled with peanut butter, the fraction of peanut butter to total filling will be three over four, three-fourths.
We’re interested in the ratio of jam to peanut butter. We have the fraction for jam to total filling and peanut butter to total filling. We could say that the ratio is one-fourth to three-fourths. But because the denominators of each of these fractions are the same, we can simplify and say that the ratio of jam to peanut butter is one to three, which is our first option: one to three.
Let’s consider one other way to think about this problem. Inside our sandwich, there are four parts. One-quarter is jam, and the rest is peanut butter. Three-fourths of the sandwich is peanut butter. And the ratio of jam to peanut butter is one to three. There is one part jam for every three parts peanut butter.